chapter 3 Waves Flashcards
What is a wave?
A regular disturbance that carries energy from one place to another
What does a wave transport?
Energy, not matter
When a wave is present in a medium, what happens to the individual particles?
They are temporarily displaced from their rest position; there is always a force acting upon the particles that restores them to their original position
What are the two ways of showing wave motion in a graph?
- displacement-time
* displacement-distance
What is displacement?
Instantaneous distance from the equilibrium (undisturbed) level
What is amplitude?
The maximum displacement from the equilibrium position
What is wavelength?
The distance between any two points on adjacent cycles which are vibrating in phase
What is the meaning of ‘in phase’?
At the same point in the cycle
What is time period?
The time taken for one complete cycle (oscillation/wave)
What is frequency?
The number of oscillations (or cycles) in one second
the equation for time period if found on the data sheet. what do the symbols stand for?
T= 1/f
T = 1/f T= time period f= frequency
the wave speed equation is found on the data sheet. what do the symbols stand for?
c =fλ
c =fλ
c= wave speed f=frequency λ=wavelength
Derivation of the wave equation?
- speed = distance / time = wavelength / period
- c = λ/T = λ/f⁻¹
- c = λf
What is phase difference?
The difference between two waves having the same frequency and referenced to the same point in time
What is phase difference expressed in?
Degrees, radians or fractions of a cycle
Would two oscillators with the same frequency and different phases have a phase difference?
Yes - they would be out of phase with each other
What is the range of values for phase difference?
- degrees - 0 to 360
* radians - 0 to 2π
What is antiphase?
When the phase difference is 180 degrees (π radians)
What is the equation for phase difference?
- x/λ x 360 (degrees)
* x/λ x 2π (radians)
What are transverse waves?
When the displacement is at right angles to the direction of the wave
What are longitudinal waves?
When the displacement is parallel to the direction of the wave
What type of wave is light?
Transverse, electromagnetic
What type of wave is sound?
Longitudinal, mechanical
What are mechanical waves?
Waves that travel by vibrating particles in a medium
Can mechanical waves travel in a vacuum?
No
What are electromagnetic waves?
Waves that can travel through a vacuum
What is the speed of light in a vacuum?
3 x 10⁸ m/s
What happens when an electromagnetic wave hits a surface?
The wave can be reflected, transmitted or absorbed
What happens to an object when it absorbs an electromagnetic wave?
Its temperature increases
In what planes can the displacements of oscillations in transverse waves be?
In all planes
What are plane-polarised waves?
Have the oscillations in one plane only
How is light polarised?
- by absorbing all planes of oscillation except one
* by reflection
What is Polaroid plastic formed from?
Many tiny crystals, all lined up
Which planes of oscillation does Polaroid plastic absorb?
All of them except the vertical one
When light is polarised by reflection, which way is the plane of polarisation?
Horizontal
What happens if you wear sunglasses made from Polaroid plastic and look at water?
Reflection off the water surface is absorbed, because its plane of polarisation is perpendicular to that of the Polaroid
Why do you not get dazzled by the reflected glare from water when wearing Polaroid sunglasses?
The plane of polarisation of the water is perpendicular to that of the Polaroid
What happens if two pieces of Polaroid are ‘crossed’ so that their transmission planes are at right angles?
No light will get through
How can transverse and longitudinal waves be distinguished?
Transverse waves can be polarised; longitudinal cannot
What are electromagnetic waves a combination of?
Electric and magnetic field waves produced by moving charges
What is polarisation used in?
- sunglasses
* alignment of aerials for transmission and reception
When are waves superposed?
When two waves of the same type are in the same place at the same time
How is the resultant displacement at any point found when two waves are superposed?
By adding displacements of each separate wave
What is interference?
The adding together of waves
What is the principle of superposition?
At a point where two or more waves meet, the instantaneous displacement (amplitude) is the vector sum of the individual displacements due to each wave at that point
When will interference be constructive?
When waves are in phase and the same frequency
What must the path difference be for constructive interference?
nλ (where n is a whole number of wavelengths)
When will interference be destructive?
When waves are in antiphase and have the same frequency
What must the path difference be for destructive interference?
(1+n/2)λ i.e. an odd number of wavelengths
What does it mean when waves are phase linked?
The waves have a constant phase difference
When are superposed waves easier to ‘see’?
- the waves are of similar amplitude (↑ contrast between maxima and minima)
- the waves have similar frequencies - otherwise the interference patterns create change so fast that they are difficult to detect
- the waves have a constant phase difference i.e. they are phase linked
Examples of coherent sources?
- light produced by a laser
- sound from two loudspeakers connected in parallel
- light emerging from two apertures illuminated by the same source
What are coherent sources?
Sources that have synchronised phase changes, as well as same frequency and λ
What are nodes?
On stationary waves, points that are always at equilibrium and 0 oscillation
What are antinodes?
On stationary waves, points of maximum oscillation
On a stationary wave, what it the distance from one node to the next?
1/2 λ
How are stationary waves formed on a string?
- vibrator moves up and down - sends travelling wave down cord
- wave reflected at end, so 2 travelling waves overlap and interfere
- has antinodes and nodes; distance between nodes = 1/2λ
What is the resonant frequency of a rubber band?
Where the band vibrates with large amplitude
Comparison of the frequencies of particles in stationary and travelling waves?
- stationary - all particles (except nodes) have the same frequency
- travelling - all particles have the same frequency
Comparison of the amplitudes of particles in stationary and travelling waves?
- stationary - varies from 0 (nodes) to maximum (antinodes)
* travelling - same for all particles
When does resonance occur?
When the frequency driving the system matches the natural frequency of the system
Comparison of the phase difference between two particles in stationary and travelling waves?
- stationary - mπ (m = no. of nodes between the two particles)
- travelling - 2πx/λ (x = distance apart)
Comparison of the energy of particles in stationary and travelling waves?
- stationary - energy stored and not transferred
* progressive - energy transferred
What is a stationary wave?
Where energy is stored rather than transmitted - formed when 2 coherent waves travelling in opposite directions interfere to produce nodes and antinodes
What can increase the pitch of a note on a guitar string?
- ↑ tightness/tension
- ↓ length of string
- ↓ thickness of string
What does the 1st harmonic depend on?
1st harmonic frequency f depends on tension T in wire, its length l and its mass per unit length
The equation to calculate the frequency of the 1st harmonic is found on the data sheet. what do the symbols stand for?
f = 1/2l x √T/μ
f = 1/2l x √T/μ f= frequency l= length (m) T= tension (m) μ= mass per unit length( kg per meter)
What happens when the air at one end of the a tube/pipe is caused to vibrate?
A longitudinal wave travels down the tube, and is reflected at the opposite end - forming a stationary wave
Where are the anti-nodes in an open pipe?
At both ends
Why are waves reflected at the ends of open pipes?
Air acts as a barrier outside
For the fundamental frequency in an open pipe, what is the pipe length?
λ/2
For an open pipe, which frequency is the first overtone?
2nd harmonic (2f₁)
What is the frequency for the second harmonic in an open pipe?
2f₁
For the second harmonic in an open pipe, what is the pipe length?
λ
What is the frequency for the third harmonic in an open pipe?
3f₁
For the third harmonic in an open pipe, what is the pipe length?
3λ/2
Which harmonics can be obtained from an open pipe?
All of them
At resonant frequencies in a closed pipe, where are the nodes and anti-nodes?
Node at closed end, anti-node at open end
Describe the amplitude of the particles in a closed pipe.
Amplitude ↓ gradually from the maximum at the open to zero at the closed end
For the fundamental frequency in a closed pipe, what is the pipe length?
λ/4
For a closed pipe, which frequency is the first overtone and what does it look like?
3rd harmonic (3f₁)
What is the frequency for the third harmonic in a closed pipe?
3f₁
For the third harmonic in a closed pipe, what is the pipe length?
3λ/4
For a closed pipe, which frequency is the second overtone?
5th harmonic (5f₁)
What is the frequency for the fifth harmonic in a closed pipe?
5f₁
For the fifth harmonic in a closed pipe, what is the pipe length?
5λ/4
Which harmonics can be obtained in a closed pipe?
Odd harmonics
Why are standing waves only produced at certain frequencies?
There needs to be a whole number of stationary wave loops fitting into the length of the string
What does the double slit interference pattern consist of?
Equidistant parallel fringes alternating between:
- maxima (constructive interference)
- minima (destructive interference)
What happens when waves are travelling in the same direction and overlap?
They interfere
What does it mean if two sources are coherent?
They emit identical waves which start in phase
How can light that is in phase be produced for the double slit experiment?
- use 2 coherent sources
* use single source with double slits
What does it mean if two sources are coherent?
They have the same frequency, wavelength and synchronised phase changes
The equation for the double slit interference pattern is found on the data sheet. what do the symbols stand for?
w = λD / s
w = λD / s
w= fringe spacing (m)
λ= wavelength (m)
D= slit to screen distance (m) (capital d is always the bigger distance)
s=spacing between slits (m)
For small angles, what does sinθ equal?
θ
If all types of wave interfere, why can’t we see interference patterns?
To obtain a clear interference pattern it requires two coherent waves of monochromatic light- light is usually emitted in bursts of waves, after which is a random phase change
How is light usually emitted?
In bursts of waves, each burst lasting 10⁻⁹s, after which there’s a random phase change
What is a monochromatic source?
A source of a single wavelength
What is usually used as a monochromatic light source?
A sodium lamp
Is there interference when two separate light sources are used?
Never
What is fringe separation?
The distance between neighbouring bright fringes
What happens to the double slit interference pattern if green light is used instead of red?
Wavelength is decreased so distance between adjacent fringes decreases
What happens to the double slit interference pattern if white light is used?
The central fringe is white, with red edges. Other fringes will be spectra with the blue end towards the middle of the overlap area
What happens to the double slit interference pattern if the screen is moved further away?
D↑ so distance between adjacent fringes increases
What happens to the double slit interference pattern if the phase difference between 2 sources is changed to 180°?
The maxima will become minima and vice versa
What happens to the double slit interference pattern if both slits are made narrower?
Wider interference so there are more dots, but fainter as there is less light through (x ↑)
What happens to the double slit interference pattern if one slit is narrower than the other?
The waves don’t fully cancel out
How can you increase x in the young’s slits experiment?
- ↑ D - measurement easier and more accurate but fringe intensity decreased
- ↓ a - practical limit to this
- ↑ wavelength
Can mechanical waves interfere?
Yes
What is diffraction?
When a wave passes through a gap and spreads out
What happens to diffraction when the gap width ↓?
Diffraction ↑
When is diffraction strongest?
When the gap with is similar to the wavelength of the wave
Why do waves passing through a single gap interfere?
- only 1 slit but more than 1 wave
- single slit can be thought of as large no. of sources next to each other
- each ‘source’ produces coherent wave - overlap and interfere
What happens, when light is shone on a diffraction grating, when the wavelength is increased?
- short λ (e.g. blue light) - narrow diffraction pattern
* long λ (e.g. red light) - broad diffraction pattern
What happens when white light is shone on the diffraction grating instead of monochromatic?
- white light yields less clear patterns (as position of dark bands depends on λ)
- colours appear; only central band is white
Difference between single and double slit pattern?
- single slit - central max. fringe that is twice the width of the other fringes
- double slit pattern has equally spaced fringes
How many slits are on a diffraction grating?
1000s
Which method produces a better diffraction pattern?
Diffraction grating - as not much light gets through the double slits so are dim and unclear
What is a diffraction grating?
A set of slits for light waves to pass through
How do you calculate the number of slits per meter on a diffraction grating?
m = 1/d
the Diffraction grating equation is found on the data sheet. what do the symbols stand for?
dsinθ = nλ
dsinθ = nλ d= slit seperation (m) theta= angle n= order of maxima λ= wavelength (m)
In the diffraction grating equation, what is the significance of sinθ never being greater than one?
There is a limit to the number of spectra that be obtained
What is the zero-order maximum?
The waves that produce the bright spot straight on - paths are all the same length, so phase difference is zero
What is the equation for the maximum number of orders?
n = d/λ
Why is sinθ not present in the equation for the maximum number of orders?
It will give a maximum when sinθ=1, so cancels out
When using the equation n=d/λ, which quantity must be a whole number?
n
Which is more accurate, the diffraction grating or the double slit method?
Diffraction grating
Why is the diffraction grating more accurate than the double slits?
- double slits - fringes formed are slightly blurred → large errors
- diffraction grating - images are clear and measurements accurate, also final result is an average of several calculations
What can diffraction gratings be used for?
Analysis of spectra
What is an optical fibre?
A long, thin, cylindrical core of glass, encased in a cladding of glass of lower refractive index
What is refraction?
A change in the direction of light as it passes across a boundary between two transparent substances
What happens, in terms of refraction, if light passes across a boundary at 90° to a surface?
It doesn’t refract
What is a refractive index?
A measure of the optical density of a material relative to air
What is the approximate refractive index of air?
1
the equationccfor the ‘refractive index of a material’ is found on the data sheet. What does each letter stand for in the equation n=c/v?
n=c/v
n = refractive index
c = velocity of light in vacuum
v = velocity of light in the medium
What is the word definition of Snell’s law?
The ratio of the sines of the angles of incidence and refraction are constant when it passes between two given media
what do the symbols stand for?
n₁sinθ₁ = n₂sinθ₂
n₁sinθ₁ = n₂sinθ₂
n= refractive index
theta= angle
What are the two conditions for total internal reflection?
- light passes from more to less dense medium
* angle of incidence > critical angle
What is total internal reflection?
When light passes from a more to less dense medium, and the angle of incidence > critical angle, all light is reflected back to the less dense medium
What is the critical angle?
The limiting angle of incidence, as the angle of refraction cannot exceed 90°
What is the angle of refraction when the angle of incidence is equal to the critical angle?
90°
the critcal angle formula is given on the data sheet. what do the symbols stand for?
sinx= n2/n1
sinx= n2/n1 x = critical angle n2= the material it diffracts into n1= the first material
How does light travel along an optical fibre?
By total internal reflection, only escaping when it reaches the other end
What is an endoscope?
A medical instrument that uses optical fibres to look inside the body
What do endoscopes consist of?
- a coherent bundle of fibres (lens system)
* an incoherent bundle of fibres (light delivery system)
What happens if a fibre is bent too tightly?
Angle of incidence will be less than critical angle and light will escape
What can endoscopes be used to look at?
Digestive, respiratory and female reproductive systems
What are the positives of endoscopes?
Can diagnose patients without an incision, often without anesthetic
In an optical fibre, when will total internal reflection occur?
As long as θ is larger than the critical angle
i.e. sin θ > n of cladding ÷ n of core
In medicine, what are the uses of optical fibres?
- endoscopes
* lasers - burn tissue to heal wound
What is a coherent bundle of fibres?
Where the fibres stay in the same relative position along their length
What are some of the problems for optical fibres?
- scratches can cause light to leak
- two fibres touching can cause light to pass from one to the other - ‘cross talk’
- dispersion
How can scratches and cross talk be resolved when using optical fibres?
Using cladding
Does cladding have a lower or higher refractive index than the core?
Lower
How is light sent down an optical fibre?
In ‘pulses’ or ‘bursts’
How can a pulse be distorted in an optical fibre?
• absorption - some energy absorbed so pulse has lower amplitude.
• dispersion - causes pulse broadening. 2 types:
modal- light enters at different angles and hence takes a different path.
material- light travels at different speeds.solved by using monochromatic light.
What are the two types of dispersion?
- material (chromatic) dispersion - light kaing different paths
- modal (multipath) dispersion- light being different speeds
How does multipath dispersion occur?
A pulse can take a variety of different paths through a fibre, meaning a single pulse can spread out over time
How can multipath dispersion be decreased?
- use monomode fibres with a core diameter of only a few wavelengths, so light travels via one path
- cladding
How can cladding help to reduce multipath dispersion?
Refractive index of cladding is only slightly lower than the refractive index of the core, so the critical angle is larger than is would be at a glass-air boundary → only small range of angles that can be transmitted
What is the diameter of a typical mono-mode fibre?
10 micrometers (1-10 x 10⁻⁶ m)
How can material dispersion be reduced?
Using monochromatic light (red will travel faster than blue)
What colour of light should be used in an optical fibre?
Red - it travels faster
What is it called when in a prism, white light is split into a spectrum of colours?
Dispersion
In a prism, what colour light is refracted more: red or blue?
Blue
Why is blue refracted more than red in a prism?
Blue light travels more slowly in glass than red light
When is pulse distortion more of a problem?
When the pulses are very short and close together
When are single fibres used?
In communications
When are bundles of fibres used?
In endoscopes
what is pitch?
Pitch is a term used to describe how high or low a note seems to be.
The pitch of a note depends on the frequency.
A high frequency produces a high pitched note and a low frequency produces a low pitched note.
what is a beat pattern?
A beat pattern is a wave whose amplitude is changing at a regular rate. Observe that the beat pattern (drawn in green) repeatedly oscillates from zero amplitude to a large amplitude, back to zero amplitude throughout the pattern.
how to derive the ‘dsinΘ =nλ’ equation?
‘dsinΘ =nλ’ equation?
<p>What is a wave?</p>
<p>The oscillation of particles or fields.</p>
<p>What is a progressive wave?</p>
<p>A wave that carries energy from place to place without transferring any material.</p>
<p>What is a wave cycle?</p>
<p>One complete vibration of a wave.</p>
<p>How do you measure the speed of sound with this setup?</p>
<p>Microphones = separate inputs so signals can be recorded separately.</p>
<p>How can you measure the wave speed in water?</p>
<p>What are the two types of graphs that can be drawn to show a transverse wave?</p>
<p>1) Displacement against distance along the path of a wave<br></br>2) Displacement against time for a POINT as the wave passes<br></br><br></br>(Note: 1 is just a standard graph of what a wave looks like. 2 is what happens to a specific point as a wave passes through it.)</p>
<p>What does the distance between two crests/troughs represent on a displacement - distance graph?</p>
<p>Displacement - distance: Wavelength</p>
<p>What does the distance between two crests/troughs represent on a displacement - time graph?</p>
<p>Displacement - time: Time period</p>
<p>What are the parts of a longitudinal wave?</p>
<p>• Compressions <br></br>• Rarefactions</p>
<p>What is a polarising filter?</p>
<p>A panel that polarised waves by only allowing a specific direction of vibration to pass through.</p>
<p>What happens when two polarising filters are arranged at right angles to each other?</p>
<p>No light will get through.</p>
<p>What happens if the two filters aren't quite at right angles?<br></br>What is done to the filter to proves this?</p>
<p>It instead reduced the intensity of the light passing through it (but still allows some light through).<br></br>By rotating the filter we can see the change in intensity:</p>
<p>How does glare work?</p>
<p>Light reflected off some surfaces is partially polarised - some of it is made to vibrate in the same direction (Figure 9).<br></br><br></br>When light reflected off surfaces like water, glass or tarmac enters the eye, it can cause glare.</p>
<p>What happens to these waves?<br></br>How do you work out the displacement of the combined wave?</p>
<p>Add the displacements of the two waves (=resultant)</p>
<p>Waves with a phase difference of 0* or a multiple of 360* are said to be...</p>
<p>... in phase.</p>
<p>Waves with a phase difference of an odd number multiple of 180* are said to be...</p>
<p>... exactly out of phase.</p>
<p>When are interference patterns most clear?</p>
<p>When the two sources are coherent (have the same wavelength and frequency and have a fixed phase difference between them).</p>
<p>Assuming that two sources are coherent and in phase, at what path difference will constructive interference occur?</p>
<p>At a whole number of wavelengths.<br></br><br></br>Path difference = nλ</p>
<p>Assuming that two sources are coherent and in phase, at what path difference will destructive interference occur?</p>
<p>At a whole number of wavelengths and a half.<br></br><br></br>Path difference = nλ + 0.5λ</p>
<p>What is a stationary wave?</p>
<p>The superposition of two progressive waves with the same frequency (wavelength) moving in opposite directions.</p>
<p>Describe how stationary waves in a string can be demonstrated.</p>
<p>• Vibration generator is attached to a piece of string at one end, while the string is fixed at the other end.<br></br>• The frequency of the generator is varied until a resonant frequency is found.</p>
<p>Describe how the wave on a fixed piece of string (so it reflects at the end) changes with frequency.</p>
<p>• At most frequencies, the pattern on the string is a jumble<br></br>• If the vibration generator produces an exact number of waves in the time it takes a wave to get to the end and back, the original and reflected waves reinforce each other. This produces a stationary wave. - The overall pattern doesn't move along, it just vibrates up and down.</p>
<p>What is a node on a stationary wave?</p>
<p>Where the amplitude of the vibration is zero.<br></br><br></br>Total destructive inteference</p>
<p>What is an antinode on a stationary wave?</p>
<p>Where the maximum amplitude of the wave is.<br></br><br></br>constructive interence</p>
<p>What is the first harmonic?</p>
<p>• When the stationary wave is vibrating at the lowest possible resonant frequency.<br></br>• One loop is on the string, with a node at each end.</p>
<p>At the first harmonic, what is the length of the section of string?</p>
<p>1/2 a wavelength of the wave</p>
<p>At the second harmonic, what is the length of the section of string?</p>
<p>1 wavelength<br></br>(when 2 half wavelengths (loops) fit on a string, the wavelength is the length of the string)</p>
<p>At the third harmonic, what is the length of the section of string?</p>
<p>1.5 wavelengths</p>
<p>What is added each time you have another harmonic?<br></br>How do you work this out?</p>
<p>an extra loop and an extra node, the number of wavelengths goes up by 1/2.<br></br><br></br><br></br>At the a^th harmonic the number of antinodes = a. number of nodes is a + 1.<br></br><br></br><br></br>At the a^th harmonic, a/2 wavelengths fit on the string</p>
<p>How can you work out the frequency of the harmonic?</p>
<p>a x first harmonic frequnecy.<br></br><br></br>a = number of antinodes or the amount of harmonics or just the amount of bumps</p>
<p>How many wavelengths are in the first harmonic for a closed tube?</p>
<p>Closed tube: the first harmonic has 1/4 wavelength.<br></br><br></br>(still increases by 1/2 a wavelength but the first harmonic starts at 1/4 wavlenghs)</p>
<p>Closed tube: how many wavelengths are in the second harmonic</p>
<p>3/4 wavelengths (0.75)<br></br><br></br>(still increases by 1/2 a wavelngth but the first harmonic starts at 1/4 wavlenghs)</p>
<p>Closed tube: how many wavelengths are in the third harmonic</p>
<p>5/4 wavelngths (1.25)<br></br><br></br>(still increases by 1/2 a wavelngth but the first harmonic starts at 1/4 wavlenghs)</p>
<p>Open tubes: What does an open tube look like?</p>
<p>Antinode at entrance and exit, normal number of wavelngths in a harmonic (1st = 1/2, 2nd = 1, 3rd = 1.5)</p>
<p>How do open and closed wavelengths compare?</p>
<p>Open tubes have more wavelength in the tube (in order to have an antinode at both ends).<br></br><br></br>This means they have a smaller wave in the same size tube.<br></br><br></br>When you hit a tube on a table with its 1 lid off, you get a deeper pitch than if it had both sides open and being hollow.<br></br><br></br>Watch TLPhysics video about closed and open tube harmonics.</p>
<p>How are stationary microwaves found?</p>
<p>• Microwaves beam reflected of a metal plate - the superposition of the wave and it's reflection produces a stationary wave.<br></br>• The nodes and antinodes are found by moving the probe between the transmitter and reflecting plate.<br></br>• The meter or loudspeaker receievs no signal at the nodes and maximum signal at the antinodes.</p>
<p>Describe how sound can be used to demonstrate stationary waves.</p>
<p></p>
<p>How do you find the speed of sound from this?</p>
<ul><li>A loudspeaker produces sound waves in a glass tube</li><li>Glass tube with a speaker at the end is set up</li><li>Lycopodium powder is laid along the bottom of the tube</li><li>The powder is shaken away from the antinodes and left undisturbed at the nodes</li><li>Distance, d, between each pile of power (node) is <strong>λ </strong>/2. ( <strong>λ </strong>= 2d)</li><li>The speed of sound = c = f<strong>λ </strong>.</li><li>c=f<strong>λ</strong> is the same as c = f x 2d which is c = 2df</li><li>You can find the speed of sound by measring d and knowing the frequnency of the signal generator</li></ul>
<p>Describe an experiment used to show how mass, length and tension change the resonant frequencies of a string.</p>
<p>1) Measure the mass and length of the string using a mass balance and ruler. Work out the mass per unit length (μ = M/L) in kg/m.<br></br>2) Set up the equipment as shown. This involves connecting a vibration generator (connected to a signal generator) to a piece of string attached to a pulley and some masses. Clamp the entire setup to the bench.<br></br>3) Measure the length (l) of the string between the vibration generator and the pulley. Work out the tension in the string using (T = mg) where m is the mass of the masses on the end of the string.<br></br>4) Turn on the signal generator and adjust the frequency until the first harmonic is found.</p>
<p></p>
<p>Depending on the experiment, you can chose to either change the mass (per unit length), the length or the tension; of the string</p>
<p>Chose one to change and keep the rest the same.</p>
<p></p>
<p>In the stationary wave experiment, what equation is used to give the FIRST harmonic frequency of a STRING?</p>
<p>f = (1 / 2l) x root(T / μ)<br></br><br></br>Where:<br></br>l = String length (m)<br></br>T = Tension in string<br></br>μ = Mass per unit length of string (kg/m)<br></br><br></br>See page 29 of revision guide.</p>
<p>Why are the 2 loudspeakers coherent sources of sound waves?</p>
<ul><li>They have the same frequency/wavelength AND constant phase difference.</li><li>This is achieved by both speakers being connected to same signal (generator)</li></ul>
<p></p>
<p></p>
<p>Point A is at equal distances from P and Q. He then moves to point B.</p>
<p>A student moves from A to B and the amplitude of the sound wave he hears decreases and then increases. The amplitude starts to decrease again as he moves beyond B. Explain why the variation in amplitude occurs as he moves from A to B.</p>
<ul><li>The sound waves from the two speakers superpose (at a point) (not interfere)</li><li>At A (and B) the two waves are in phase (they have zero phase difference) and a maximum is produced.</li><li>Moving away from A introduces a path difference/phase difference = waves are out of phase (and amplitude decreases)</li><li>Minima's are formed when there is destructive interference (odd number of half wavelength = path difference or π/ 180 degrees = phase difference or antiphase)</li><li>(Moving on towards B the waves move back in phase)</li></ul>
<ul><li>separation of the two loudspeakers = 0.30m</li><li>distance OA = 2.25 m</li><li>distance from A to B = 0.95 m</li><li>Show that the path difference for the sound waves from the two loudspeakers to point B is about 0.1 m.</li></ul>
<p>The frequency of the sound wave is 2960 Hz. Calculate the speed of sound from the student’s data.</p>
<p>(remember path difference = 0.12 meters)</p>
<p>Path difference between two maxima's = 1 wavelength.</p>
<p>1 path difference = 0.12 m</p>
<p>1 wavelength = 0.12 m</p>
<p>0.12 x 2960 = 360m/s</p>
<p></p>
<ul><li>As frequency increases, so does wavelength.</li><li>Therefore, the separation of maxima's (along the line AB) increases</li><li>Maximum moves (from B) towards C so amplitude of sound gets larger/louder (then quieter). OR Maximum moves further along path/beyond C so amplitude of sound gets quieter.</li></ul>
<p></p>
<p>How can you show this (picture) with an experiment?</p>
<p>Use two microwave transmitter cones attached to the same signal generator.</p>
<p>Use a microwave receiver probe - you get an alternating pattern of strong and weak signals.</p>
<p>How can you demonstrate young's double slit experiment?</p>
<p>What are the safety precautions?</p>
<p>How can you investigate the formula of young's double slit experiment with this set up?</p>
<p>In the exam, you are given n = c/cs. Practise deriving the two equations for relative refractive index from this.</p>
<p>• n = c/cs<br></br>• 1n2 = c1/c2 (It's logical from the definition!)<br></br>•1n2 = n2/n1</p>
<p>What is the angle of incidence and what is the symbol?</p>
<p>The angle that incoming light makes to the normal.<br></br>Symbol: θ1</p>
<p>What is the angle of refraction?</p>
<p>The angle that the refracted ray makes to the normal.<br></br>Symbol: θ2</p>
<p>Which was does light bend when it enters a more optically dense material?</p>
<p>From this, if n1 < n2, what can we say about θ1 and θ2</p>
<p>Towards the normal.</p>
<p>Which was does light bend when it enters a less optically dense material?</p>
<p>From this, if n1 > n2, what can we say about θ1 and θ2</p>
<p>Away from the normal.</p>
<p></p>
<p>How do you get the critical angle?</p>
<p>How can we find the refractive index of a material if the boundary is material to air and we have the critical angle?</p>
<p>What is total internal reflection?</p>
<p>When light going from a more optically dense to a less optically dense material hits the boundary at an angle greater than the critical angle and is completely reflected.</p>
<p>Describe how an optical fibre works.</p>
<ul><li>Step index optical fibres used</li><li>The fibre has a very high refractive index (optically dense), but is surrounded by a cladding with a lower refractive index (less optically dense) -> This enables TIR + Protects the fibre.</li><li>The fibre is narrow -> Light always hits the boundary at an angle greater than the critical angle.</li><li>Light that enters at one end is totally internally reflected to the other end</li></ul>
<p></p>
<p>What are the 2 reasons for making an optical fibre thin?</p>
<p>• Ensures light hits at angle above the critical angle
| <br></br>• Prevents modal dispersion</p>
<p>How does light get from 1 end of the fibre to the other?</p>
<p>What is signal degradation by absorption and how does it affect the signal?</p>
<p>• Some of the signal's energy is lost through absorption by the material of the fibre.
<br></br>• This reduces the amplitude.</p>
<p>What is pulse broadening?</p>
<p>The recieved signal is boader than the initial signal. Broadened pulses can overlap each other, leading to information loss</p>
<p>What is modal dispersion and how does it affect the signal?</p>
<p>• Light rays enter the fibre at different angles and so take different paths -> Some arrive later than others. Rays taking a path straight down the middle of the fibre arrive faster than rays taking a longer path.<br></br>• This causes pulse broadening.</p>
<p>What is material dispersion and how does it affect the signal?</p>
<ul><li>Caused by different amounts of refraction experienced by different wavelengths of light</li><li>Different wavelengths slow down by different amounts in the material so they travel at different speeds in the fibre -> Some arrive later than others.</li><li>This causes some parts of the signal to take a longer time to travel down the fibre than others.</li><li>This causes pulse broadening.</li></ul>
